1. Field of the Invention
The present invention relates to a method of modifying uniformity of tire, in details, to a method of reducing the second harmonic of TFV (tangential force variation) which is one of factors for causing vehicular vibration in high speed running of an automobile.
2. Description of the Related Art
Vehicular vibration such as vibration of a steering wheel caused in high speed running of an automobile, is caused by being inputted with force variation of tire owing to unevenness referred to as tire nonuniformity or force variation in centrifugal force caused by rotation of tire based on unevenness of mass of tire in its circumferential direction referred to as unbalance in correspondence with a vibration characteristic of suspension or the like of a vehicle. Among them, in respect of vibration of the first harmonic of tire rotation, there have been proposed a method concerning its mechanism and improvement.
For example, in respect of force variation caused by mass unbalance in the circumferential direction of tire, the variation is reduced by attaching a balance weight to a road wheel. Further, in respect of the first harmonic of TFV or radial force variation (RFV) caused by a variation in the diameter of tire, the variation is reduced by reducing force variation or diameter variation in the circumferential direction of tire.
Meanwhile, in respect of the second harmonic or higher harmonics, although they are normally small and not problematic, their levels are increased by an increase in the running speed of an automobile, further, they are considerably increased when the frequencies of the harmonics coincide with the resonance frequency of tire in high speed running.
Particularly, in respect of the second harmonic of TFV, a resonance frequency of a longitudinal torsional vibration of tire is at a vicinity of 25 through 40 Hz and accordingly, a frequency of the second harmonic of tire rotation and the longitudinal torsional resonance frequency coincide with each other at a vicinity of normal running speed of 100 km/h at high speed running, hence, the second harmonic of TFV increases significantly to thereby constitute a factor of generating vehicular vibration.
However, in respect of the second harmonic of TFV, its mechanism of occurrence and method of improvement thereof have not been clarified and even when a balance weight is attached to a road wheel similarly to reducing the force variation by unbalance, the second harmonic of TFV is not reduced.
Therefore, conventionally, a position of a seam of material is changed in producing tire or promoting accuracy of production steps, as a result, the second harmonic of TFV is reduced.
In view of such an actual situation, it is an object of the invention to reduce the second harmonic of TFV constituting one factor of vibration in high speed running of a vehicle.
As a result of an intensive study by ascribing the second harmonic of TFV to mass unbalance in the circumferential direction of tire and diameter variation in the circumferential direction, the inventors have found that the second harmonic of TFV is reduced by providing or eliminating masses at pertinent two locations opposed to each other in the diameter direction of tire and completed the invention.
That is, according to a first aspect of the invention, there is provided a method of modifying uniformity of tire wherein a tire is rotated at a vibration generating speed based on the second harmonic of TFV and a phase and an amplitude of the second harmonic are measured, and wherein the second harmonic of TFV is reduced by providing mass members specified based on the amplitude at two locations opposed to each other in a diameter direction of the tire specified based on the phase such that the measured second harmonic of TFV is canceled by the second harmonic of TFV caused by providing the masses.
More specifically, the measured phase of the second harmonic of TFV is converted into the first harmonic phase of the tire and the mass members are provided within a range of 32.0 through 61.0 deg in a rotational direction in measuring the second harmonic from tire positions minimizing the second harmonic by which the second harmonic of TFV can be reduced.
According to a second aspect of the invention, there is provided a method of modifying uniformity of tire wherein a tire is rotated at a vibration generating speed based on the second harmonic of TFV and a phase and an amplitude of the second harmonic are measured, and wherein the second harmonic of TFV is reduced by eliminating masses specified based on the amplitude at two locations opposed to each other in a diameter direction of the tire specified based on the phase such that the measured second harmonic of TFV is canceled by the second harmonic of TFV caused by eliminating the masses.
More specifically, the measured phase of the second harmonic of TFV is converted into the first harmonic phase of the tire and the specified masses are eliminated within a range of 32.0 through 61.0 deg in the rotational direction in measuring the second harmonic from tire positions maximizing the second harmonic by which the second harmonic of TFV can be reduced.
Next, a detailed description will be given of the operation of the invention.
In the case in which there causes mass unbalance in the circumferential direction of tire, as shown by FIG. 3, when the tire is rotated, unbalance force based on unbalanced mass m is caused by centrifugal force and TFV is caused by a component thereof TF in the longitudinal direction.
The longitudinal direction component TF of the centrifugal force of the unbalanced mass m is given as follows by acceleration xcex1Z in the diameter direction and acceleration xcex1X in the circumferential direction.
TF=m(xcex1X cos xcex8+xcex1Z sin xcex8)xe2x80x83xe2x80x83(1)
In this case, the accelerations xcex1X and xcex1Z are measured by an inner face acceleration meter, changed in accordance with a position xcex8 of the unbalanced mass m and is increased before and after grounding as shown by FIG. 4. This is because the substantial radius is changed when the unbalanced mass m is grounded. Owing to such a change of the accelerations xcex1X and xcex1Z, even when there causes mass unbalance of the second harmonic at two locations (a state in which unbalanced masses are present at two locations opposed to each other in the diameter direction of tire), these are not canceled by each other.
Hence, as shown by FIG. 5, assume that unbalanced masses m are present at two locations opposed to each other in the diameter direction (phase=0 deg, 180 deg) on the circumference of the tire, TFV is calculated by calculating the longitudinal direction component TF of the centrifugal force of the unbalanced masses m by Equation (1) mentioned above and the result of calculation is subjected to Fourier analysis to thereby calculate the amplitude and the phase of the second harmonic of TFV. In that case, in respect of the magnitude of TF, magnitudes of respective frequency components are corrected in consideration of the transmissibility in the longitudinal direction of the tire.
The result is shown by FIG. 5 and in FIG. 5, the phase of the second harmonic of TFV is shown to be converted into the first harmonic phase of the tire. As shown by FIG. 5, according to the second harmonic of TFV, peak positions (positions having maximum values) P thereof are disposed at two locations opposed to each other in the diameter direction of 46.5 deg and 226.5 deg as tire positions and bottom positions (positions having minimum values) B are present at positions (136.5 deg and 316.5 deg) of a phase difference of 90 deg as tire positions from the peak positions P.
It is known thereby that according to the second harmonic of TFV caused by mass unbalance, the peak position P is provided with shift of phase of xe2x88x9293 deg from the position of the unbalanced mass m or rearward therefrom by 46.5 deg in a rotational direction in measuring the second harmonic as tire position. The fact signifies that by providing masses at two locations opposed to each other in the diameter direction of tire, there causes the second harmonic of TFV having peak positions rearward from positions of the masses by 46.5 deg as tire position and bottom positions forward therefrom by 43.5 deg.
In order to confirm the fact by an experiment, the second harmonic of TFV at a running speed of 100 km/h was measured by a high speed uniformity machine by using a radial tire for a passenger vehicle having a tire size of 175SR14.
In the experiment, from a waveform of the second harmonic of TFV in the case in which the second harmonic was measured by providing masses at two locations opposed to each other in the diameter direction of the tire, a waveform of the second harmonic of TFV in the case where the second harmonic of the tire was measured with the tire as it was, was subtracted by which a waveform which was changed by providing the masses was calculated and amplitude and phase thereof were calculated.
As a result, according to the second harmonic of TFV caused by providing the masses, the peak position was provided with shift of phase of about xe2x88x92100 deg from the position of the mass or rearward therefrom by about 50 deg in the rotational direction in measuring the second harmonic as the tire position and it was confirmed that a result equivalent to that of the above-described simulation was obtained.
A predetermined second harmonic of TFV can be caused by providing masses at two locations opposed to each other in the diameter direction of the tire in this way and accordingly, by aligning the bottom positions of the second harmonic of TFV caused by providing the masses to the peak positions of the second harmonic of TFV of the tire which have been calculated by the measurement, the second harmonic of TFV of the tire can be reduced.
In details, by providing mass members within a range of 46.5 degxc2x114.5 deg from the bottom positions of the measured second harmonic of TFV in the rotational direction in measuring the second harmonic as the tire position, the measured second harmonic of TFV of the tire is canceled by the second harmonic of TFV caused by providing the masses and as a result, the second harmonic of TFV of the tire can be reduced.
Meanwhile, the mass unbalance caused by the masses provided at two locations opposed to each other in the diameter direction as shown by FIG. 5, can be grasped as mass unbalance caused by deletion of masses d caused by eliminating the masses at positions with a phase difference 90 deg from the positions of providing the masses (90 deg, 270 deg) as shown by FIG. 6. Accordingly, it signifies that by eliminating masses at two locations opposed to each other in the diameter direction of tire, there causes the second harmonic of TFV having bottom positions B rearward from positions of eliminating the masses by 46.5 deg as a tire position and peak positions P forward therefrom by 43.5 deg.
By eliminating masses at two locations opposed to each other in the diameter direction of tire in this way, a predetermined second harmonic of TFV can be caused and accordingly, by aligning bottom positions of the second harmonic of TFV caused by eliminating masses to peak positions of the second harmonic of TFV of tire which has been calculated by measurement, the second harmonic of TFV of tire can be reduced.
In details, by eliminating masses within a range of 46.5 degxc2x114.5 deg in the rotational direction in measuring the second harmonic as tire position from peak positions of the measured second harmonic of TFV, the measured second harmonic of TFV of the tire is canceled by the second harmonic of TFV caused by eliminating the masses and as a result, the second harmonic of TFV of the tire can be reduced.
Further, although the second harmonic of TFV is caused not only by the mass unbalance in the circumferential direction of the tire but by diameter variation in the circumferential direction of the tire, the second harmonic of TFV can be reduced regardless of such factors of generating the second harmonic by providing or eliminating masses at two locations opposed to each other in the diameter direction as mentioned above.